Cylindrical capacitors with gas dielectrics

ABSTRACT

In a cylindrical capacitor having a gaseous dielectricum the relation between the coefficient of expansion of the material of the inner cylinder of the capacitor and the gas pressure, which is held steady, being such as to make the capacity of the capacitor substantially independent of temperature variations within the operational temperature range of the capacitor.

United States Patent Boersma et al.

CYLINDRICAL CAPACITORS WITH GAS DIELECTRICS inventors: Rintie Boersma, l-larmelen; Huibert A. J.

M. Spoorenberg, Utrecht, both of Netherlands Assignee: N. V. COQ", Utrecht, Netherlands Filed: Oct. 23, 1969 Appl. No.: 868,763

Foreign Application Priority Data 1,422,312 7/1922 Smith ..3 17/244 1,545,207 7/1925 Smith ....3l7/244 1,610,980 12/1926 Silberman..... ....3 17/242 1,881,164 10/1932 Bailey ..3l7/242 2,271,983 2/1942 Larue ..317/247 X OTHER PUBLICATIONS The Condensed Chemical Dictionary Sixth Edition Reinhold 1963 p. 1093.

Primary Examiner-E. A. Goldberg Attorney-Imirie, Smiley, Snyder & Butrum ABSTRACT 7 Claims, 2 Drawing Figures nllpdllraull 0.

/ 111/ 1/ ll/l/ Mar. 20, 1969 Netherlands ..6904281 US. Cl. ..3l7/244, 317/247, 317/258 Int. Cl. ..1101g 3/02 Field oi Search ..3l7/242, 244, 247, 258

References Cited UNITED STATES PATENTS i 2 I I I I I I a A I Q g a t l g N I 5 h g Q 1 t 5' s 1 q 5 E w PATENTEUFEBZS I972 FIGJ IVENTOR BOERSMA Rial-rm: NUI'BERT A. J. N. SPOORENBERG M'L Jami} I ATTORNEY I I V 2 r u CYLINDRICAL CAPACITORS WITH GAS DIELECTRICS i 1 p 1 I TQ p l I 7 1 r I. 0 Theinventionrelates to'a cylindrical capacitor for. highvoltr age havingagaseous dielectricum. Therein is k a constantof the material peratmosphere of the iln'switehgear for high voltages not only voltage tranetorpressure, .T..the chosen-reference temperature in K. degrees mersbutalso capacitive voltage dividerlare'usedfor measurd gh f h as i m h said pressure 'ingztpurposes. Such devices are safer for'dir'ect connections being heldsteady.

with the live condllcm" and y P) COnSidflab'X less At a variationof the temperature the dimension of the-and roomthan W 8 transformers Capacitive "Olmge dividers distancebetw'een the-capacitor electrodesvary. The influence calibc "Provided with resonance circuits with p of these variations'on the-capacity of the capacitor will appear The voltage dividers provided with resonance circuits are fromthe'following alulmion g y dependem'onfl'equency Variations in network, 50 If the capacitor'has, at the reference temperature T a that they aresuitablerfor less accurate measurements only. l hj outer di Rwandan inner ,radius one m The capacitive voltagedividers provided with amplifiers have fi d uh temperature T that; i the disadvantage'thatthe transmission ratio of the capacitor 1 1, [1+ 1. 1 circuit is dependent on the temperature which is highly varia- R R [1+ 1 1 blein switchgear, say from -C. to +80.C. i r r0 7 10)] The'invention haszthe object to providea cylindricalcapaci- I torwhich is-suitable-foruse in capacitive voltage-dividers proare and the coefficients ofexphhsloh .vided with amplifiersor othercircuitsfor accurate measurelo'ofime material of the cylinder and the material of the ments and in which, due to special measures, the capacity ihher cyhhdeh Fhrthehhorh h is assumed h length variation within the interesting temperature range remains of the-capacltor defined by the outer cyhhder only If below the value of 0.1 percent required for accurate'measure- T To: the capacity of the capacitor he at the merits. This is achievedin that at a chosen reference tempera- 3993 .1 ture the ratio between the radius of the inner electrode surface of theouter cylinder of the capacitorand the radius of the outer electrode surface of the inner cylinder of the capacitor is 2 equal to'the base e of the natural logarithm, whereas the inner 1 cylinder consists mainly of material having such a linear coefr MAT) e s expanse" and the P of the gaseous dlelec- TEWaHaraEed that at thereferericetemperatncum is'kept constant or substantially constant at such a I ture T the ratio betweenR and r is equal to thebase e of the value as ensure that natural logarith, so that i ln B3 1.

T,T2 kpT The denominator'of equation 2) will then be l+ln(-l-oz AT)-ln( l+a AT). If aqAT and a AT are small in respect of i, it maybe assumed that 'ln( 1+a,AT) =a,AT and ln( l+a,AT)

in which'a is said coefficient of expansion, k is a material constant-of thc gasper atmosphere of the pressure, p is said pres- .igg h3232:2213?32:51 }f gg i zg g gxggt zn =a A-T. lfthese values are entered in'equation 2), one will find peratures inK; degrees of a temperature range which is equal 40 (that 277 1 (1 AT) or lies'within the'temperature range, in which the temperature t 2 of the capacitor is apt to vary during normal operation. 5 C =W 'The meaning of the conditions stated here above will appear a 1 I 2 from-thefollowing calculation.

or 1 I Y .-:-----f'--- The capacity of a cylindrical ca acitor is 2w 2 lo (1 a1 AT) (1 0! AT MAT) 277' 2 2 1 i C 0 r R i 1-(a AT-omAT) Since mAT and (LAT are small in respect of I, all square There nW =0 h 'dl l t constant of a Vacuum, =r the powcrsthereofmay be-neglected, so that equation 2) changes dielectric constant of the gaseous 'dielectricum and 1 the mm; length, R the radius-of the inner electrode surface of the outer 2 -5 5 +azAT) cylinder an'd'r the radius of the outerelectrode surfaceof the inner cylinder of the capacitor. The-quantities 5,, l, Rand r ,,5 5', 3 are dependenton'the temperature T. v s lfequation 1 is inserted in equation 3) one will find that:

'I'he'variation of i depends, according to a relatr'ons'hip kT which'will' be given hereafter, on the variation of the density 0' C 2 21,,(1 ){1 (1 (T T,,)} (4) of if the pressure p in the capacitor'must be held o T steady, gas will have to be discharged from the capacitor vessel, when 'the temperature rises, and gas will have to be supplied to the capacitor vessel, when the temperature falls. In the first-case the density and the dielectric-constant decrease and in thesecondcase-these quantities increase. In each situation It follows therefrom that the=expansion of the outer cylinder has a negligible effect on the capacity of the capacitor and that, as aconsequence thereof, only the materialof the inner cylinder has to be reckoned with.

The invention has the object to choose such a gas pressure p 5 'and a material for the inner cylinder withsucha'linear coefficient of expansion 01, that a'capacitoris 'obtained, of which, even when the capacitor is used for accurate measurements, :is-constant-andgince thedensity ais inverselyproportional to w Fapaeity varies negligibly when. the varies tl'lespecificvolume'v. also 0' Twill be constant. Assuming the iwnhm the temperatine i found normal openmon and density a, to-belong'to the chosen reference temperatureT 'thegas'presshre vanes the range defined by the densityawill be defined at any other temperature T by sitiyiityofvthe for hbldihgthe gas pmssure steady Since at'a' variation of the temperature T the value of the term T 0' 1 nP The dielectric constant of a gas is defined by the equation: T

v,only. If these temperatures T, and T have been selected the relation between the coefficient of expansion or, and the gas pressurep will be found by means of the equation z The greatest errors are made, if the temperatures T, and T are the extreme temperatures of the interesting temperature range. Smaller errors are possible, if the temperatures T, and T lie in given points within said temperature range, said points being not calculated more fully, I The capacitor constructed in accordance with the invention is especially meant for use in the mentioned voltage dividers, which are particularly adapted for measurements in high-voltage switchgear. In such switchgear the temperature is able to vary between 20 C. and +80 C., so that the interesting temperature range extends from 253 to 353 K. If the gas in the capacitor is air, the constant k has, at the reference tempera ture T,,=293 K., the value of 55.10" per atmosphere of the pressure, If the inner cylinder of the capacitor is made of aluminum, the coefficient of expansion 01 is equal to 24.10 per "C. It then follows from equation 6) that the gas pressure p must have the value of 13.4 atmospheres, if it is required that the capacitor has, at 253 K., the same capacity as at 353 K.

If a =24. 10' and p 13.4 atmospheres, the capacity of the capacitor at the temperatures T,=253 K. and T 353 K. can be calculated with the aid of equation 4). Said capacity is found to be: C= 211E 1 1,00757.

At a temperature lying between the extreme temperatures T, and T the compensation is not exact. For instance at the temperatures T=** K. and T=3 13 K. it is found that:

C1 21rE,,l,,. 100,737 61 Zia-5 1,100,737

Thus the error on a percentage basis is both at T= 293 K.

and at T=313 K. about equal to abut 1,0075? atmospheres about 1,0075? 100% 0,0337%,

At T= T 353 K. and p 14.4 atmospheres the capacity will be:

C 21rE,,1,,. 100,802 The error on a percentage basis will then be about None of these errors appear to be more than 0.l percent, so that the capacitor is adapted to be used for measurements for which an accuracy of 0.1 percent is required.

If. in order to obtain 0 greater strength against rupture or to 4 be able to decrease the radial dimension of the capacitor, a higher air pressure, say a pressure of 20 atmospheres, has to be used in the capacitor a material having an other coefficient of expansion a, must be used for the inner cylinder of the capacitor. This coefficient of expansion is determined by equation 5) and it will be 35.7.10'. Then the inner cylinder may be made of synthetic resin, of which the outer surface is provided with a metal layer forming the capacitor electrode.

In stead of air an other gas, e.g., sulfur-hexafluoride (SR-gas) may be used in the capacitor. This gas, which is used in switchgear for very high-voltages, has a great strength against rupture, but it condenses at the prevailing temperatures at rather low pressure. If the temperature can fall, as in the former case, to 20 C. the pressure may not be higher than 4 atmospheres, since otherwise condensation will occur. The constant k of SF gas is 2.3.10 per atmosphere of the pressure. If a gas pressure p of 2 atmospheres or of 4 atmospheres is used, one will find with the aid of equation 5) for the coefficient of expansion at, of the material of the inner cylinder of the capacitor:

a 2992.10 In the first case said inner cylinder may be made of a copper alloy and in the second case of a metallized synthetic resin, e.g., cast resin.

However, if the inner cylinder is made of aluminum having a coefiicient of expansion or: 24.10' and if the dielectricum consists of SF,,-gas, the required pressure is calculated with the aid of equation 6). One then finds that p is about 3.2 atmospheres.

It (assimilates that as; in in; 50050312555851;

which the dielectricum of the capacitor consists of SF gas, the variation of the capacity due to a variation of the temperature within the interesting temperature range from 253 to 353 K. and to a variation of the pressure within the sensitivity range of the device for holding the pressure steady will remain below 0.1 percent, so that also such a capacitor can be used in a capacitive voltage divider for accurate voltage measurements.

The drawing shows,

FIG. 1 an axial sectional view of a cylindrical capacitor con: structed in accordance with the invention and,

FIG. 2 on a larger scale an axial sectional view of a part of a differently formed inner cylinder of such a capacitor.

In FIG. 1 the reference numeral 1 designates a closed vessel which is filled with an insulating gas under overpressure. The vessel 1 is connected to a conduit 2 leading to a device (not shown) to hold the pressure of said gas steady. Mounted in the vessel is a cylinder capacitor which consists of an inner cylinder 3 and an outer cylinder 4. At least the outer surface of the inner cylinder and at least the inner surface of the outer cylinder are electrically conductive. A conductor with bushing insulator 5 is provided for the electric connection of the inner cylinder 3 and a conductor with bushing insulator 6 is provided for the electric connection of the outer cylinder 4. The inner cylinder 3 is supported by the bushing insulator 5 and a supporting insulator 7 and the outer cylinder 4 is carried by welded collar rings 8, 9.

At the reference temperature T,,, which may be 20 C. (293 K.) the ratio between the inner radius R of the outer cylinder 4 and the outer radius r.of the inner cylinder 3 is equal to the base e of the natural logarithm, that means about 2,7 I 8.

In the embodiment shown in FIG. 2 the inner cylinder 10 consists of synthetic resin, e.g., cast resin, of which the outer surface is provided with a thin electrically conductive layer ll, e.g., is metallized.

What we claim is:

l. A cylindrical capacitor for high voltage and which may be subjected to temperature variations over a specified temperature range during normal operation, comprising a hollow outer cylinder. an inner cylinder mounted concentrically in said outer cylinder and a gaseous dielectric, at least the inner surface of the outer cylinder and at least the outer surface of the inner cylinder being electrically conductive and constituting the electrodes of the capacitor, the ratio between the radius of the inner surface of the outer cylinder and the radius of the outer surface of the inner cylinder being, at a given reference temperature T,,, equal to the base e of the natural logarithm, the linear coefficient of expansion a of the main substance of the inner cylinder and the pressure p, at which the gaseous dielectric is held substantially steady, being selected to provide equal capacitances at temperatures T and T which are within said temperature range and being given by the equation kpT a T1 T2 kpT in which a is said coefficient of expansion, k is a constant of the substance of the gas per atmosphere of the pressure of the gas, p is said pressure in atmospheres, T is said reference temperature in K. degrees and said temperatures T and T are in K. degrees.

2. A cylindrical capacitor as claimed in claim 1, in which the inner cylinder consists mainly of aluminum and the dielectric consists of air.

3. A cylindrical capacitor as claimed in claim 1, in which the inner cylinder consists mainly of synthetic resin, an electrically conductive surface layer forming the inner electrode of 6. A cylindrical capacitor as claimed in claim 1, in which the inner cylinder consists of a copper-alloy and the dielectric consists of SF gas.

7. A cylindrical capacitor for high voltage, which capacitor provides relatively constant capacitance over a temperature range to which the capacitor may be subjected, comprising;

a hollow outer cylinder having at least an inner'electrically conductive surface of uniform radius R constituting one electrode of the capacitor;

an inner cylinder mounted in said outer cylinder and having at least an outer electrically conductive surface of uniform radius r constituting the other electrode of the capacitor and which is concentrically spaced with, respect to said inner surface;

the space between said electrodes being filled with a gaseous dielectric maintained at a substantially constant, selected pressure p;

the ratio,

of the radii of said inner and outer surfaces at a reference temperature T,,, which is within said temperature range, being equal to the base e of natural logarithms whereby values of capacitance of said capacitor are substantially independent of dimensional changes of said outer cylinder due to variations in temperature to which said capacitor may be subjected; and

said value of p and the coefficient of expansion of the main substance of said inner cylinder being selected to provide equal capacitances between said electrodes at temperatures T, and T which are respectively above and below said reference temperature T and are in said temperature range. 

1. A cylindrical capacitor for high voltage and which may be subjected to temperature variations over a specified temperature range during normal operation, comprising a hollow outer cylinder, an inner cylinder mounted concentrically in said outer cylinder and a gaseous dielectric, at least the inner surface of the outer cylinder and at least the outer surface of the inner cylinder being electrically conductive and constituting the electrodes of the capacitor, the ratio between the radius of the inner surface of the outer cylinder and the radius of the outer surface of the inner cylinder being, at a given reference temperature To, equal to the base e of the natural logarithm, the linear coefficient of expansion Alpha of the main substance of the inner cylinder and the pressure p, at which the gaseous dielectric is held substantially steady, being selected to provide equal capacitances at temperatures T1 and T2 which are within said temperature range and being given by the equation in which Alpha is said coefficient of expansion, k is a constant of the substance of the gas per atmosphere of the pressure of the gas, p is said pressure in atmospheres, To is said reference temperature in K. degrees and said temperatures T1 and T2 are in K. degrees.
 2. A cylindrical capacitor as claimed in claim 1, in which the inner cylinder consists mainly of aluminum and the dielectric consists of air.
 3. A cylindrical capacitor as claimed in claim 1, in which the inner cylinder consists mainly of synthetic resin, an electrically conductive surface layer forming the inner electrode of the capacitor being provided on said inner cylinder, and in which the dielectric consists of air.
 4. A cylindrical capacitor as claimed in claim 1, in which the inner cylinder consists mainly of synthetic resin, an electrically conductive surface layer forming the inner electrode of the capacitor being provided on said inner cylinder, and in which the dielectric consists of sulfur-hexafluoride (SF6-gas).
 5. A cylindrical capacitor as claimed in claim 1, in which the inner cylinder consists mainly of aluminum and the dielectric consists of SF6-gas.
 6. A cylindrical capacitor as claimed in claim 1, in which the inner cylinder consists of a copper-alloy and the dielectric consists of SF6-gas.
 7. A cylindrical capacitor for high voltage, which capacitor provides relatively constant capacitance over a temperature range to which the capacitor may be subjected, comprising; a hollow outer cylinder having at least an inner electrically conductive surface of uniform radius R constituting one electrode of the capacitor; an inner cylinder mounted in said outer cylinder and having at least an outer electrically conductive surface of uniform radius r constituting the other electrode of the capacitor and which is concentrically spaced with respect to said inner surface; the space between said electrodes being filled with a gaseous dielectric maintained at a substantially constant, selected pressure p; the ratio, , of the radii of said inner and outer surfaces at a reference temperature To, which is within said temperature range, being equal to the base e of natural logarithms whereby values of capacitance of said capacitor are substantially independent of dimensional changes of said outer cylinder due to variations in temperature to which said capacitor may be subjected; and said value of p and the coefficient of expansion of the main substance of said inner cylinder being selected to provide equal capacitances between said electrodes at temperatures T1 and T2 which are respectively aBove and below said reference temperature To and are in said temperature range. 